#Q67If two sets A and B having 99 elements in common then number of elements common to each of the sets A×B and B×A are
Anonymous Quiz
21%
2^99
67%
〖99〗^2
9%
100
3%
18
#Q69 If |A|=m, |B|=n,& |A∩B|=r then |(A×B)∪(B×A)|=
Anonymous Quiz
11%
mn
32%
mn-r^2
53%
2mn-r^2
5%
2mn-2r
#Q70 Consider the following relation R on the set of real square matrices of order 3. R={(A,B):A=P^(-1) BP for some invertible matrix P } Then
Anonymous Quiz
4%
R is not reflexive
57%
R is an equivalence relation.
33%
R is an equivalence relation.
6%
R is an equivalence relation.
#Q71 Which of the following statement is false.
Anonymous Quiz
19%
If S is an open set and T is closed set. Then S-T is always open set
21%
Non empty countable set cannot be open
40%
Limit point of a set S can also be an interior point of S^c
21%
Limit point of a set cannot be an interior point of S^c
#Q72 Let A={〈a_n 〉 ∶ a_n=1 for finitely many value of n} Consider a set S⊆R which is similar to A. Then which of the following is/are true?
Anonymous Quiz
7%
S must have condensation point
41%
S may have condensation point
33%
S must have limit point
19%
S may have limit point
#Q73 A={y:y=x-|x|,x∈R} and B={y:y=x+|x|,x∈R} Then which of the following is true.
Anonymous Quiz
17%
A∪B is open but not closed
41%
A∪B is only closed not open
38%
A∪B is both open and closed
3%
None of these
#Q74 Which of the following set is not dense in IR.
Anonymous Quiz
16%
{m+n√2,m,n ∈Z }
24%
{m/2^n ,m∈Z,n∈Z}
25%
{m+ne:m,n∈ Z}
35%
{cos〖n:n∈N〗 }
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June 2016 CSIR NET MS Question Paper With Answer Key.pdf
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Dec 2015 CSIR NET MS Question Paper With Answer Key.pdf
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Dear Friends , Today Quiz will start at 3:00 PM. Total 10 Questions - Part B - Mathematical Science. Thanks
#Q76 Let S is the set of all numbers of the form 2^(-P)+3^(-q)-5^(-r) where p,q and r∈Z^+, then
Anonymous Quiz
12%
Sup S=0,Inf S=-1
53%
Sup S=31/30,Inf S=0
24%
Sup S=30/31,Inf S=1/30
12%
None of these
#Q77 If m and M are respectively the greatest lower bound and the least upper bound of the set S={(2x+3)/(x+2);x≥0} then
Anonymous Quiz
27%
m∈S,M∉S
31%
m∉S,M∉S
18%
m∉S,M∈S
24%
m∈S,M∈S
#Q75 A={y:y=x-|x|,x∈R} and B={y:y=x+|x|,x∈R} Then which of the following is true
Anonymous Quiz
24%
A∪B is open but not closed
29%
A∪B is only closed not open
43%
A∪B is both open and closed
4%
None of these
#Q78 The least upper bound of the set {(n+1)^2/2^n∶n∈N} is
Anonymous Quiz
8%
7/4
44%
2
44%
9/4
4%
5/2
#Q79 The set {x∈R:x sinx≤1,x cosx≤1}⊆R is
Anonymous Quiz
43%
A bounded closed set
22%
A bounded open set
23%
An unbounded closed set
12%
An unbounded open set
#Q80 Let A be a subset of [0, 1] with non-empty interior and let Q+A={q+a:q∈Q,a∈A}. Which of the following is true?
Anonymous Quiz
22%
Q+A=R
48%
Q+A can be a proper subset of R
20%
Q+A need not be closed in R
11%
Q+A need not be open in R
#Q81 Let X be a proper closed subset of [0,1]. Which of the following is always true?
Anonymous Quiz
17%
The set X is countable
41%
There exist x∈X such that X\\{x} is closed
36%
The set X contains an open interval
6%
None of these
#Q82 Which of the following is/are correct?
Anonymous Quiz
29%
Under continuous map image of an open set is open
20%
Under continuous map image of closed set is closed
42%
Under continuous map pre image of open set is open
9%
Under continuous map pre image of closed set is closed
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